"John Henry" is an old folk song, Beck probably learned it off of Woody Guthrie. I say "learned" cautiously, because Beck, after the first verse, forgets the rest. He proceeds to whistle the vocal melody a bit, before whistling "You Are My Sunshine" instead.

Beck's loose cover can be found a very informal tape made of what seems to be him and some friends singing songs at a house party or something, circa 1990.